a Fermi National Accelerator Laboratory FERMILAB-conf-89/253-A December 1989

The Age of the Universe: Concordance

David N. Schramm

University of Chicago 5640 S. Ellis Avenue

Chicago, Illinois 60637 and

NASA/Fermilab AstrophyGcs Center Femi National Accelerator Laboratory

Boz 500 Batavia, Illinois 60510

ABSTRACT

Arguments on the Age of the Universe, t,, are reviewed. The four independent age deter- mination techniques are:

(1) Dynamics (Hubble Age and deceleration); (2) Oldest stars (globular clusters); (3) Radioactive dating (nucleocosmochronology); (4) White dwarf cooling [age of the disk).

While discussing all four, this review will concentrate more on nucleocosmochronolog due in part to recent possible controversies there. It is shown that all four techniques are in general agreement, which is an independent argument in support of a catastrophic creation event such as the Big Bang. It is shown that the most consistent range of cosmological ages is for 12 5 t. 5 1’7Gyr. It is argued that the upper bound from white dwarf cooling is only N 1OGyr due to the disk of the Gaxaxy probably forming several Gyr after the Big Bang itself. Only values of the Hubble constant, H,, 5 GOkm/sec/Mpc, are consistent with the other age arguments if the universe is at its critical density. An interesting exception to this limit is noted for the case of a domain wall dominated universe where ages 89 large as 2/H0 are possible.

Proceedings of talk delivered at the 5th IAP A&ophysies Meeting, “Astrophysical Ages and Dating Methods, n In&d d’Astrophysique de Paris, June 26-29, 1989.

s Opwatml by Unlverslties Remarch Association Inc. under contract with the United States DqWtment Ot En*rSY

Introduction

The age of the universe can be estimated by four independent means:

1. Dynamics (Hubble age and deceleration)

2. Oldest Stars (globular clusters)

3. Radioactive Dating (nucleocosmochronology)

4. White Dwarf Cooling (age of the disk)

All four of these techniques have been discussed at this Institut d’Astrophysique sym-

posium on “datation.” This paper will focus on radioactive dating and on the concordance

of the four techniques. We will see that despite much work over the last couple of decades,

the basic picture is still a total age of about 15 Gyr with an uncertainty of several Gyr.

While trends come and go in each technique, the uncertainties continue to allow this range

of concordance. If R = 1, as most cosmologists believe, then concordance does seem to

favor small values for H, (5 GOlcm/sec/Mpc). Furthermore, the age of the disk may really

be significantly lower than the age of the universe (tdiait s lOGyr), which may be telling

us something quite interesting about galaxy formation.

As to nucleochronology itself, much attention has focused on new production estimates

and on the measurements in stars, but when all the smoke clears away, the basic relatively

independent model conclusion remains solid, namely, a strong lower bound of about 9 Gyr

from the lowest mean age and a “best-fit” galactic evolution dependent age of 12 to 18

Gyr.

Although all of the techniques are reviewed in other papers in this proceedings, for

completeness and to show the author’s viewpoint, this paper will briefly describe the

results of each of the four techniques. However, the discussion of nucleochronology will be

somewhat more detailed. The paper will then discuss the problems of concordance and

make its conclusions.

The Age from Dynamics

The use of the Hubble constant to determine an age is the most quoted and least

accurate of all the age determination methods. ‘Detailed references are given in other

papers in this volume, so they won’t be repeated here. Let us merely note that astronomers

continue to get values ranging from Ho - lOOkm/sec/Mpc down to values near Ho -

dOkm/sec/Mpc. The higher values tend to come from people using techniques like TuIley-

Fisher, whereas the smaller values come from people using supernovae. A critical question

tends to be the accuracy of intermediate distance calibrators and the correction for infall

into the Virgo cluster. Most of us can’t see anything wrong at face value with the Tulley-

Fisher techniques other than a possible susceptibility to the so-called Malmquist bias.

However, many physicists have a certain fondness for the use of Type-I supernovae as

standard candles. Type I’s seem to be due to the detonation of a C-O white dwarf star

converting its C-O to Fe. Such a model has a physical relationship between its luminosity

and basic nuclear quantities that can be measured in the lab. Current best-fit models

(c.f. Nomoto) tend to convert about 0.7M@ of C-O, which yields Ho - GOkm/sec/Mpc.

However, even in the extreme where the entire 1.4M0 Chandrasekhar msss is burned, H, is

never below 38km/sec/Mpc. Sandage and Tammann’s empirical calibrations which ignore

the nuclear mechanism yield Ho - 42km/sec/Mpc, which fsIl within the theoretically

allowed range and correspond to almost complete burning of a Chandrasekhsr core. While

selecting between 42 and 60 is still a matter of choice, it does seem that values less than 38

can be reliably excluded. Why these numbers disagree so much with the best Tulley-Fisher

determinations of about 80 remains to be understood.

Age, t,, is related to H, by:

t _ f0-v “--H, (1)

where for standard matter-dominated models with A = 0.

R=O f(Q) = $3 R=l

- 0.5 n = 4 and smoothly varies between those values. The parameter fl is the cosmological density

IOGyr parameter. A range of 40 s Ho 5 lOOkm/secfMpc yields 1OGyr 5 l/H, 5 WGyr.

Ftom dynamics alone we can put an upper limit on 51 by limiting the deceleration

parameter pO. From limits on the deviations of the redshift-magnitude diagrams at high

redshift, we know that q 5 2 (for zero cosmological constant R = 2q.,. Thus we can argue

that R 5 4 or that f(n) 2 0.5. Therefore, from dynamics alone, with no further input, we

can only conclude that

5 5 t. s 25Gyr (2)

Since the lower bound here could also be obtained from the age of the earth, it is clear

that the dynamical technique is not overly restrictive unless one could somehow decide

between the supernova approach and TUley-Fisher. Hopefully some of this dispersion

should collapse when the Hubble space telescope flies and one can use cephieds in the

Virgo cluster to remove many of the uncertainties in the intermediate distance calibrators.

An interesting loophole in the t. -H., relationship occurs in a domain wall dominated

universe. Hill, Schramm and FYy (1989) have argued that late-time phase transitions can

produce domain w&s which could generate the large-scale structure of the universe. The

energy density in walls scales is N l/R’+’ where e is dependent on wall evolution. For

0 5 e 5 1, the resluting t, - H, relationship for (Cl = 1) is t, = & where 1 5 f’ 5 2 (c.f.

Massarotti 1989).

Thus, high values of H, can be consistent with high ages without invoking the cosmo-

logical constant if the universe is wall-dominated. (Such models also stretch out the age

vs. redshift relationship, enabling longer times for galaxy formation.) Press, Ryden and

Spergel (1989) have shown that A44 wall models evolve to single horizon-size walls and

thus are ruled out by the microwave isotropy. However, Hill, Schramm and Widrow (1989)

show that sine-Gordon walls or walls from multiple minima avoid such problems, as do the

texture models of Turok (1989).

The Age from the Oldest Stars

Globular cluster dating is an ancient and honorable profession. The basic age comes

from determining,how long it takes for low mass stars to burn their core hydrogen and

thereby move off the main sequence. The central temperature of such stars is determined

by their composition and the degree of mixing. While there has certainly been some static

as to what is the dispersion between the age of the youngest versus the oldest globular

cluster in a given calculation, there is a surprising convergence on the age of the oldest

clusters. Since the age of the very oldest cluster is the critical cosmological question,

it is really somewhat of a red herring as to how much less the youngest cluster may

be. The convergence on the age of the oldest does require a consistency of assumptions

about primordial Helium and metalicity (including O/Fe). Difference between different

groups can be explained away once agreement is made on these assumptions. For example,

Sandage’s oldest ages of 18-19 Gyr and Iben’s of 16-17 Gyr are consistent if the same

Helium is used. (The lower range is more consistent with the current primordial Helium

measurements of Pagel, 1989.) Another decrease of a billion years occurs if O/Fe is assumed

high ss current observations show. The best ages for the oldest globular clusters seem to

be around 16 Gyr with a generous spread of zt3Gyr allowed. It should be noted that most

other variations in assumptions, other than the compositional ones already mentioned,

tend to go towards longer rather than shorter ages. For example, any mixing will increase

the age since the standard model assumes a radiative non-mixed core. Mixing brings in

more otherwise unburned material so that it takes longer to deplete the core’s hydrogen.

The quest& of the range in age of globulars is import& for relating globular ages to

the ages of the disk and for models of cluster and galaxy formation. Whether or not the

age spread is less than 1 Gyr or more like 5 Gyr doesn’t change the basic point that the

oldest globulars are 16 rt 3 Gyr.

Since in principle globulars can form within s 1Osyr of the Big Bang, we can use the

age .of the oldest globulars to argue that

t, - 16 f 3Gyr (3)

Of course, some models may take up to a Gyr to form the first globulars, but that is still

in the aliowed noise window.

White Dwarf Cooling Ages

The newest addition to age determination techniques is white dwarf cooling rates. The

point that there is a paucity of cool white dwarfs can be used to set a limit on the age of

the disk of our Galaxy. Of course, this age is dependent on assumptions about the rate

of cooling of single white dwarfs, the initial mass function and time dependence of star

formation rates and the estimation of what volume of space has been fully surveyed. While

the paucity problem has been known for some time, the fist, comprehensive look at the age

implications was Winget et al. They argued that the age of the disk was td 5 10Gyr. To

escape this bound one must argue that the assumptions are wrong in one way or another.

One must be careful in relating this bound to the age of the universe. Clearly, jt is some

sort of lower limit, but the quesiton is: how long did it take to form the Galactic disk?

One possible resolution of this might come from looking at cool white dwarfs in the halo.

Unfortunately, the data is still sparse, but there is some indication of lower temperature

ones, thus implying a longer age for the halos. A further argument on an extended time

span between the Big Bang and disk formation is the difference between this age and the

globular cluster ages. Another recent indication that the disk may form late comes from

the observations of Gunn (1989) and York (1989) w h o each argue that disks do not seem

to exist at redshifts 2 - 1. Since the matter era age at redshift Z(n = 1) is

t, - tll

(1 + .2)3/Z

the Gunn/York observations mean disks did not form until %.

For t,, - 15Gyr, this yields td - lOGyr, consistent with the white dwarf arguments.

Nucieocosmochronology

Nucleocosmochronology is the use of abundance and production ratios of radioactive

nuchdes coupled with information on the chemical evolution of the Galaxy to obtain in-

formation about time scales over which the solar system elements were formed. Typical

estimates for the Galaxy’s (and Universe’s) age as determined from cosmochronology are

of the order of 9 -18 Gyr (e.g. Meyer and Schrsmm, 1986). In recent years questions about

the role of B-delayed fission in estimating actinide production ratios as well ss uncertainties

in 1s7Re decay due to thermal enhancement and the discussion of Th/Nd abundances in

stars have obfuscated some of the limits one can obtain. In particular, we note that the

formalism of Schrsmm and Wasserburg (1970) as modified by Meyer and Schramm (1986)

continues to provide firm bounds on the mean age of the heavy elements. In fact, Th/U

provides a 6rm lower limit to the age and Re/OS a firm upper limit. These limits are based

solely on nuclear physics inputs and abundance determinations. To extend these mean age

limits to a total age limit requires some galactic evolution input. However, as Reeves and

Johns (1976) first showed, and as Meyer and Schramm (1986) developed further, one can

use chronometers to constrain Galactic evolution models and thereby further restrict the

age from the simple mean age limits of Schramm and Wasserburg. To try to push further

on such ranges and give ages to &lGyr accuracy, as some authors have done, always neces-

sitates making some very explicit assumptions about Galactic evolution beyond the pure

chronometric arguments. At the present time such model-dependent ages are not fully jus-

tified and should probably not be used as arguments to question (or support) cosmological

models.

Let us review what can be said from the nuclear physics without making too many

specific model-dependent assumptions.

The linearized equation for the time dependence of the abundance Ni of nuclide i in

the interstellar medium of the Galaxy (Tinsley 1975; see also Hainebach and Schramm

197’7 and Symbalisty and Schramm 1981) is

dNi(t) - = -AiNi(t) dt

- w(t)Ni(t) = R+(t)%

where X is the decay rate of nuclide i, w(t) is a time-dependent parameter representing

the rate of movement of metals into and out of the interstellar medium for resons other

than decay, $(t) is the amount of mass going into stars per unit time, and Pi is the number

of nuclei i produced per unit mass going into stars.

It is now possible to solve for the abundance Ni of nuclide i at a given time by inte-

gration of equation (5). This is done in the context of the scenario for evolution of the

material making up the solar system shown in the figure. In the figure, T is the time of

the last event contributing to formation of the elements going into the solar system, A is

the time interval between this last nucleosynthetic event and the s&lifkation of the solar

system solid bodies, and t,#(= 4.55 Gyr) is the age of these solid bodies. In this scenario,

A is a free decay period for the elements, and, consequently, we might choose to measure

meteoritic abundance back to t = T. Meteoritic material is a closed system only after

time t + A. This material thus gives abundances at times as early as 2’ f A with minimal

uncertainty due to chemical fractionation, but not before. Integration of the equation for

Jle” i i ; I 1

I I

I

0 tv T TtA t-c

NOW

Figure 1. Schematic diagram showing the effective nucleosynthesis rate as a function of time.

The quantity 2’ is the total duration of nucleosynthesis, and t, is the mean time for the

formation of the elements; A is the time interval between the end of nucleosyntheais and

solidiiication of solar system bodies; t,, is the age of the e&r system solid bodies. The total

age of the elements is T + A $ T,,.

time t = 0 to t = T followed by free decay over an interval A, yields

Ni(T + A) = Pielp(-XiA)esp[-XiT - V(T)] /’ $(t)esp[Xit + v(t)dt, (6) 0

where

v(t) = J

oiw(E)&

and we have assumed Pi to be independent of time.

Age estimates from radionuclides are obtained frrst by expansion of the normal&d

effective nucleosynthesis rate q+(t), defined as

in moments p (detied below) about the mean time for formation fo the elements t,, given

by

J

* t, = ti(t)dt.

0 With this mean time, the moments p are defined as

(8)

pn = J

*(t - ty)nq4(t)dt. 0

Meyer and Schramm (1986) find (analagously to Schramm and Wasserburg 1970) an

expression for the mean age of the elements as measured back from t = T:

T _ t, = A~= _ A + txi +2)/Q + CA: + x’xs) + xj)fi3

+g - m,2)( x; - x; &xj)+--’

where

Anar ~ “‘-1 _ InR(i, j) :, Xi - Xj = Ai _ xj (11)

(10)

and where the subscript j denotes a second radionuchde, distince from nuclide i.

Clearly, T - t, in equation (10) depends upon 4(t) through the moments p; thus, we

require some information about the effective nucleosynthesis rate if we are to continue.

We may proceed in one of two fashions. We may choose a specific form or model for 4(t),

in which case our results will be modeLdependent. Alternatively, we may attempt to find

external forms for o(t) that will allow upper and lower limits to be placed on T essentially

independently of any model for d(t). This latter tack is the one described below.

First, we note that since the moment terms in equation (10) increase 2’ - t, over

AZ” - A, a lower limit on T is given by

TEAM”-A. (12)

This is the long-lived limit of Schrarnm and Wasserburg and gives a model-independent

lower limit on the time for nucleosynthesis. With knowledge of t,/T, the lower limit is

pushed up to

T 2 (1 _ ;)-‘(Amaz - A). (13)

We derive limits on tY/T below. In principle, nucleochronology alone is not able to give

a firm upper limit to an age as was demonstrated by Wasserburg, Schramm and Huneke

(1969) who found consistent ages of 2 lOi yrs. However, by using our constraints on

average rates, some statements can be made, assuming that production was relatively

smooth with no large gaps. For an upper limit on T, Meyer and Schramm find that

T 5 (1 - tJT)-‘(Am’= - A)( 1 + c)

where e, which represents the correction to the long-lived limit, is constrained as

(14)

e S i( I- tv/T)-‘( Xi + Xj)(A”“” - A)( I+ e)’

+&(I - ty/T)-‘(XT 7 XiAj + X;)(A” - A)‘(1 + c)”

+&(l - t.,T)-‘;‘,+~~;(a-~ - A)3(1 + t)” + . . . (15) 3

With limits on t,/T, equation (15) can be solved and, hence, limits on T will be avail-

able from equations (13) and (14). Meyer and S&r- develop such limits on 1,/T in a

method inspired by the work of F&eves and Johns (1976). Fist, an average nucleosynthesis

rate < $J > ri, i over the interval ri 5 t 5 T is defined:

(16)

Then, through use of equation (16) analogous expressions for nuclides j, and variation

over all possible intervals ri 5 t 5 T and rj 5 t 5 T, it is found that

e(-h-AjW (1 _ e-&TT) A. -I < < $ >i < e(xi-xj)A Xi

R(i,j) (1-emXiT) Xj - <$>j - R(i,j) X,’ (17)

where we choose T to be its smallest possible value, namely, that given by equation (12).

The ratio of average rates < $ >i / < $ >j constrained in equation (17) is useful

because it determines the general trend of $e” over a few lifetimes of nuclide i. Thus,

since Xi > Xj, if < $e” >i / < $ >jC 1, then $e” was generally falling over a few times

ri, and if < 21 >; / < 11, >j> 1, then $e’ W&S generally rising over a few times ri.

To obtain constraints on t,/T, we define r(i, j) as the ratio < II, >i / < (I >j. We

assume a set of m chronometers. We label the longest by i = 1, the next longest by i = 2,

and so on, to the shortest-lived, labeled i = m. We then have as constraints on $e”

$e” = r(i,l) for ti-1 5 t 5 ti,

where i runs from 1 to m, ti is defined as

ti = F(Pi - ri+!), * and t, = T.

From the above, constraints on tY/T are available, viz.,

t” 1 Cz”=, r(i, I)[(ri - ri = l)‘] T = 2 Ti Cy!=, r(j, l)(rj - rj + 1)’

Use of upper limits on r(i, j) give an upper limit on t,/T. For lower limits on t,/T, Meyer

and Schramm choose to use two chronometers in a slightly d&rent fashion to obtain

L -= r(2,1) - d3Zj T r(2,l) - 1 ’

Use of lower limits on r(2,l) gives lower limits on t,/T. Similarly, upper limits on r(2,l)

can give upper limits on tY/T.

With constraints on 1,/T, we can, given the requisite input data, derive limits on T

and TGAL from the fact that

We turn now to a discussion of the input data.

In Table 1 we present best estimates of decay rates, the ratios R(i,j), and resulting

Amar dues for the Re/Os, ThfU, UjiY, and PufU chronometric pairs. The text that

follows gives a brief discussion of the uncertainty in these data.

A. RefOs

The long-lived chronometric pair 18’Re/‘8’0s is unique because ‘*‘OS is stable. Since

Xj = 0, and since A”“” > A (see Symbrdisty and Schramm who iSnd A s 0.2Gyr), we

may write equation (IS), through use of equation (ll), as

c 5 i(l - $)-z(InR(187,187)](1 + e)* + &((‘nR(‘87,187)]*(1$ e)3

+-&( 1 - $)-4[hR(i87, 187)]~(1 + e)4... (18)

The only necessary data, then, are R(187,187) and Xrsr (to get A;“a”?:r3,). R(187,187) is

given by (Schramm 1974)

R(lS7,187) = 1 + ‘:y$$ _..

where ( ‘s70s)c is the r-process contribution to ‘*‘OS.

Unfortunately, both R(187,187) and Xrsr are uncertain quantities. Bound state ,C

decay of ‘*‘Re occurring due to astration may greatly enhance the decay rate over the lab

rate (Takahashi and Yokoi 1982; Yokoi, Takahash.i and Amould 1983). Detailed galactic

evolution models are thus required to determine the amount of astration of le’Re and,

consequently, the effective decay rate of ‘*‘Re. This is difficult and uncertain work. We

note instead that the effect of astration is always to increase ,J,rsr. Thus, from equation

(11) we obtain an upper limit on A~r~rsr. We also emphasize that E in equaiton (18) is

independent of Arsr.

The uncertainty in R(187,187) arises from two sources. First, a low-lying, excited

nuclear state in ls’Os complicates the determination of (r8’Os)c (Fowler 1973; Holmes et

al. 1976; Woosley and Fowler 1979). Second, s-process branchings in the W - OS region

(Amould 1974; Amould, T&ah&i and Yokoi 1984) may contribute to the uncertainty in

R(187,187). The range on R(187,187) found by Meyer and Schramm from the anaiaysis of

Yokoi et al. and meteoritic data of Luck, Brick and AlIegre (1980) is 1.06 s R(187,187) s

1.14. The numbers of Amould et al. lead Meyer and Schramm to the larger range 1.03 ;5

R(187,187) 5 1.23. Meyer and Schramm rely mainly on the former range for R(187,187),

but also consider the effects of the latter range. Use of cross section data from Winters et

al. (1980) and a best value for the cross section correction factor f. of 0.82 (Winters 1984)

gives a best R(187,187) of 1.12. The lab Xrsr is 1.59+~:~:zlO-“yr-’ (Liider et al. 1986).

The bottom line here is that one should not ignore lBTRe but use it as an upper bound.

Table 1 Cosmochronological Input Data and Pammaters

Pair Xi( Gyr-‘) Xj(Gyr-‘)

187Re/1870~ 0.0159(+0.0005, -0.0004)

232W230U 0.0495 (+o.oooo, -0.0000) 0.1551 (+0.0002, -0.0002) 235 u/230 u 0.985 (+0.009, -0.009) 0.1551 (+0.00002, -0.00002)

244W23EU 8.47 (+0.27, -0.27) 0.1551 (+0.0002, -0.0002)

Pair R(i,j) A”‘=(Gyr)

‘s7Re/‘a70s 1.03-1.23 1.8-13.4 232T,,/238U 0.65( f0.09) 4.1 (+1.4, -1.2)

23aLr/23aU 4.7 (+1.3, -0.9) 1.9 (fO.3, -0.3)

112 (+138. -92) 0.57 (+0.12, -0.21)

B. Th/U

Beta-decayed fission is the cause of the largest amount of uncertainty in 232Th/238U

production ratio. The calculations of Thielmann et al. give 1.4 as the production ratio.

The calculations of Meyer et al. (1985) give less delayed fission and, hence, suggest a

higher production ratio. Although Meyer et al. do not include barrier penetration in their

calculations, a fact which suggests that their production ratios may be too large, their

results seem to be favored by Hoff’s (1986) study of yields from thermonuclear explosions.

The implication appears to be that less delayed fission occurs than that given by Thielmann

et al. We thus conclude that Meyer and Schramm’s use of the Thielmann et al. value

of 1.4 as a lower limit on the Th/U production ratio is justified. With the probability

of some p-delay fission, 1.7 is probably a reasonable upper limit with 1.55 as a good

compromise. They also argue from terrestrial isotopic lead ratios and meteoritic ratios

that the present solar system value for 232Th/238U is 3.9 z!c 0.2. The relevant decay rates

are X232 = 4.95slO-“yr-’ (J&ey et al. 1971).

c. up Meyer and Schramm choose the Schramm and Wasserburg production ratio range

l.Si”,:t as the best range for 235U/23sU. The range contains the Thielmann et al. value of

1.24.

The 235U/238U abundance ratio is well-known. Meyer and Schrsmm take it to be

l/(137.88 f 0.14). X335 = (9.8485 zk 0.0135)~10-‘0yr-’ (JafTey et al. 1971).

D. Pu jU

The 244 Pu/ 238U pair is the pair most affected by delayed fission. Meyer and Schramm

use the Thielmann et al. value of 0.12 as a lower limit and the Symbalisty and Schramm

upper limit 1.0 (no delayed fission) as an upper limit with 0.56 as a compromise best value.

The abundance ratio is 0.006 f 0.001 (Hudson et al.), although Meyer and Schrsmm

note that the abundance ratio range may be more uncertain than this. Xsha = 8.47 &

0.27~10-~yr-’ (Fields et al. 1968).

Meyer and Schramm derive a range on t,/T of 0.43 5 tY/T 5 0.59. From this range

and data from Table 1 for Th/U, we find a lower limit on TGAL of 9.6 Gyr. Also, from

the range 1.06 5 R(187,187) 5 1.14, Meyer and Scbrsmm derive an upper limit on TGAL

of 28.1 Gyr.

The range on tY/T agrees with the results of Hainebach and Schramm’s (1977) study of

detailed galaxy evolution models. In those models studied, Hainebach and Schrsmm found

that steady synthesis seemed to be the best approximation to the chemical evolution of

the Galaxy. Thus, tY/T = 0.50 suggests itself as the best value. If we then use tY/T = 0.05

and A?i;:,38 = 4.1 Gyr, the best value for Th/U from Table 1, we 6nd T 2 12.8 Gyr. Use

of t,/T = 0.05 and R(187,187) = 1.12 gives T 5 19.8 Gyr.

The best values range of 12.8Gyr 5 TGAL 5 19.8Gyr essentially agrees with other age

estimates (e.g. Symbalisty and Schramm, Yokoi et al.). Yet, even though it is a relatively

large range (7.8 Gyr), it does not include the allowed Galactic evolution models or input

certainties. The range 9.6Gyr 5 TGAL 5 28.1Gyr includes the cosmochronological allowed

galactic models and shows that the effect of these uncertainties is large. One may conclude

from these results that nuclear cosmochuonology, so simple in conception, is rendered quite

diEcult in practice because of input data uncertainties. It should be noted that any author

who gives smaller ranges from nucleochronology is making some implicit assumptions about

the chemical evolution of the Galaxy, and so, such ages are not pure nuclear dating. (They

are also probably underestimating the uncertainty in the production rate determination

process.)

Another recent input into the radioactive dating process has been the reported Th/Nd

observations in stars (Butcher 1987). Unfortunately, the initial ages reported were very

model dependent (Mathews and Schramm 1987). Since Nd is not a pure r-process nucleus,

interpreting this ratio can be difficult. As Page1 notes, one might try to use a pure r-process

nucleus instead of Nd to avoid this problem. Preliminary efforts at this type of analysis

seem to yield relatively low ages 5 15Gyr. Of course some have questioned the observation .

of Th itself, so it is still a bit premature to be forced to the short time end of the range

for chronology. However, this is a development that should be watched and placed in the

framework for consistency.

Consistency: A Scenario

The first point to note is that these four very independent techniques all yield ages

that overlap in the 10 to 20 Gyr range. That such an agreement occurs at all is in some

sense an independent confirmation of the basic Big Bang cosmological model!

At a more discriminating level, let us note that the best nucleochronologic models cou-

pled with Galactic evolution as constrained by nucleochronology and the globular cluster

ages tend to imply ages in the mid-teens. It is very difficult to get the oldest globular cluster

to be 5 12Gyr. Ages t,*k 12Gyr are consistent with H, 585 if R = 0. However (ignoring

wslls for the moment), if 0 = 1, such ages only are consistent with H, 5 GOkm/sec/Mpc.

Furthermore, H0 2 40kmjseclMpc is only consistent with t, < 17Gyr for R = 1.

For overall consistency, most cosmologists would probably prefer a low value of HO.

Let us hope that with HST the H, range converges to such values, otherwise we might be

forced to such ugliness as a non-zero cosmological constant but tuned to an accuracy of

parts in - 10120 when measured in its natural (Planck) units or the exotic possibility of a

domain wall dominated universe.

A universe with an age in the mid-teens (and a small H,) still has to have disks form

late if we are to be consistent with the white dwarf cooling argument. A several Gyr delay

between the Big Bang and disk formation should tell us a lot about galaxy formation in

general. If true, it would tend to argue against making galaxies as one large collapsing

isolated system, but instead, it would require some disturbances to keep the disk from

forming. One reasonable method to create such disturbances is colhsions. Perhaps the

earliest condensations were not of galaxy size but smaller. These protogalaxies collapsed

and made stars which started both the nucleochronology clock and the globular cluster

clock, but not the disk closk. A high density of these prom-galaxies as implied by Tyson’s

observations would yield a high early collision rate. Such collisions would prevent disk

formation. Eventually the density of objects would drop and collisions would cease so

that the large merged galactic mass clumps would be able to form disks. Note that in

this scenario stars formed in the proto-galaxies would naturally end up in the halo of the

final galaxy. If such stars formed with a mass function peaked either higher or lower than